The proton–proton chain makes two electron neutrinos for every helium nucleus. Neutrinos (see leptons, hadrons and quarks) feel only the weak force, so almost every one of them flies straight out of the Sun, and straight through Earth.
Why it works
Light from the core needs on the order of $10^{5}$ years to random-walk out. Neutrinos cross the Sun in about 2 seconds and reach us about 8 minutes after they are made. So they show what fusion in the core is doing now. Their number follows from the luminosity: two neutrinos per 26.7 MeV, so $$\dot N_\nu = \frac{2L_\odot}{26.7\text{ MeV}} = \frac{2(3.83 \times 10^{26}\text{ W})}{4.28 \times 10^{-12}\text{ J}},$$ about $1.8 \times 10^{38}$ neutrinos per second.
Key idea
About $6.4 \times 10^{14}$ solar neutrinos cross every square meter at Earth each second (about $6 \times 10^{10}$ per cm²), day and night. Detectors catch only a handful. The solar neutrino problem, that experiments found too few electron neutrinos, was solved by neutrino oscillations: neutrinos change flavor on the way, which means they have mass.
The history in brief
- From the late 1960s, Raymond Davis's chlorine tank deep in the Homestake mine in South Dakota counted only about a third of the predicted electron neutrinos.
- Either the solar models or our understanding of neutrinos had to be wrong. Helioseismology kept confirming the models.
- Super-Kamiokande in Japan reported neutrino oscillations in 1998, and in 2001–2002 the Sudbury Neutrino Observatory in Canada measured all three flavors together: the total matched the solar models.
- The work earned Nobel Prizes in 2002 (Davis and Masatoshi Koshiba) and 2015 (Takaaki Kajita and Arthur McDonald).
Worked examples
Worked example: Neutrinos through your thumbnail
How many solar neutrinos pass through 1 cm² each second at Earth?
- Flux: $1.8 \times 10^{38}/(4\pi(1.496 \times 10^{11}\text{ m})^2) = 6.4 \times 10^{14}$ per m² per second.
- $1\text{ cm}^2 = 10^{-4}$ m².
Answer: About $6 \times 10^{10}$ per second, some 60 billion, without effect.
Worked example: News from the core
How long after they are made do the neutrinos reach Earth?
- They cross the Sun at nearly $c$ in about 2.3 s, then travel $1.496 \times 10^{11}$ m.
- $t = 1.496 \times 10^{11}/3.00 \times 10^{8} = 499$ s.
Answer: About 8.3 minutes, so a neutrino detector watches the core in close to real time.
Common mistake
Thinking neutrinos are blocked by the Sun's layers, like light. Light interacts with charged particles constantly and random-walks out over a long time. Neutrinos interact only through the weak force; a neutrino of solar energy would typically pass through light-years of lead before stopping. Check: solar neutrino detectors work the same at night, with all of Earth between them and the Sun.